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Assembly of systems having maximum reliability

Author

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  • Cyrus Derman
  • Gerald J. Lieberman
  • Sheldon M. Ross

Abstract

The first problem considered in this paper is concerned with the assembly of independent components into parallel systems so as to maximize the expected number of systems that perform satisfactorily. Associated with each component is a probability of it performing successfully. It is shown that an optimal assembly is obtained if the reliability of each assembled system can be made equal. If such equality is not attainable, then bounds are given so that the maximum expected number of systems that perform satisfactorily will lie within these stated bounds; the bounds being a function of an arbitrarily chosen assembly. An improvement algorithm is also presented. A second problem treated is concerned with the optimal design of a system. Instead of assembling given units, there is an opportunity to “control” their quality, i.e., the manufacturer is able to fix the probability, p, of a unit performing successfully. However, his resources, are limited so that a constraint is imposed on these probabilities. For (1) series systems, (2) parallel systems, and (3) k out of n systems, results are obtained for finding the optimal p's which maximize the reliability of a single system, and which maximize the expected number of systems that perform satisfactorily out of a total assembly of J systems.

Suggested Citation

  • Cyrus Derman & Gerald J. Lieberman & Sheldon M. Ross, 1974. "Assembly of systems having maximum reliability," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 21(1), pages 1-12, March.
    • Handle: RePEc:wly:navlog:v:21:y:1974:i:1:p:1-12
    DOI: 10.1002/nav.3800210102
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    Cited by:

    1. Xiaoyan Zhu & Way Kuo, 2014. "Importance measures in reliability and mathematical programming," Annals of Operations Research, Springer, vol. 212(1), pages 241-267, January.
    2. Michael Katehakis & Ingram Olkin & Sheldon Ross & Jian Yang, 2013. "On the life and work of Cyrus Derman," Annals of Operations Research, Springer, vol. 208(1), pages 5-26, September.
    3. V.D. Dinopoulou & C. Melolidakis, 2001. "Asymptotically optimal component assembly plans in repairable systems and server allocation in parallel multiserver queues," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(8), pages 732-746, December.
    4. Coit, David W. & Zio, Enrico, 2019. "The evolution of system reliability optimization," Reliability Engineering and System Safety, Elsevier, vol. 192(C).
    5. Zhao, Jiangbin & Si, Shubin & Cai, Zhiqiang, 2019. "A multi-objective reliability optimization for reconfigurable systems considering components degradation," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 104-115.

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